Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T21:53:32.485Z Has data issue: false hasContentIssue false
  • English
  • Français

NONOSCILLATION OF ELLIPTIC INTEGRALS RELATED TO CUBIC POLYNOMIALS WITH SYMMETRY OF ORDER THREE

Published online by Cambridge University Press:  01 May 1998

LUBOMIR GAVRILOV
LUBOMIR GAVRILOV
Affiliation:
Laboratoire Emile Picard, CNRS UMR 5580, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France
Get access

Abstract

We study zeros of elliptic integrals I(h)=∫∫H[les ]hR(x, y)dx dy, where H(x, y) is a real cubic polynomial with a symmetry of order three, and R(x, y) is a real polynomial of degree at most n. It turns out that the vector space [Ascr ]n formed by such integrals is a Chebishev system: the number of zeros of each elliptic integral I(h)∈[Ascr ]n is less than the dimension of the vector space [Ascr ]n.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 3 , May 1998 , pp. 267 - 273
Copyright
© The London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)